Under many circumstances an acoustic or electromagnetic signal is received from a moving source and information as to the location and velocity of the source is desirable. Examples of where this occurs are undersea surveillance and radar surveillance. A common method of representing this is on a graph known as an ambiguity plane, where distance is plotted against velocity. The relative doppler shift and time shift between two signals so received can be used to extract this data.
The ambiguity plane is prepared by evaluating the ambiguity integral which is defined as EQU .chi.(.omega.,.tau.)=.intg.dt f.sub.1 (t)f.sub.2 *(t-.tau.)e.sup.i.omega.t ( 1)
In this equation f.sub.1 (t) and f.sub.2 (t) are the two signals being compared expressed as functions of time. The variable .tau. is introduced to correct for the fact that although it is expected that f.sub.1 (t) and f.sub.2 (t) should have a similar form, they will, in general, be shifted in time relative to each other. The function f.sub.2 *(t-.tau.) is the complex conjugate of f.sub.2 (t-.tau.) which is the time shifted version of the signal actually received. The factor e.sup.i.omega..tau. is introduced to correct for the frequency difference between f.sub.1 (t) and f.sub.2 (t), caused by the doppler effect. The values of .omega. and .tau. which yield a maximum value of the ambiguity integral may be used to extract information about the velocity and range of the object under surveillance.
In order to be useful for surveillance purposes the information displayed on an ambiguity surface must be as current as possible. For this reason evaluation of the integral (1) must be performed in real time. The ability of optical analog processing to process multiple channels of data rapidly in a parallel fashion has led to its acceptance as a method for ambiguity function calculations. One such method is shown in the copending application, Ser. No. 105,809, now U.S. Pat. No. 4,310,894, assigned to the same assignee as the instant invention.
Most prior art ambiguity processors have suffered inaccuracies because they have operated on the doppler shift of the carrier frequency, but have not dealt with the time scaling of the modulating function. One system which does consider the time scaling of the modulating function is described in U.S. Pat. No. 4,123,142 issued to Fleming et al. The system of the Fleming patent requires the construction of the "channelized" lens, which is more complicated and difficult to construct than the lenses of the present invention. It also provides values of the ambiguity integral only for discrete values of .tau. rather than the continuum provided in the present invention.